Non-values of $a^3 + b^{c^3} - 3 a b c$ for $a,b,c\in\mathbb{N}$ like $n$ for prime $19n+17$? I stumbled on a curious case of Richard Guy's Strong Law of Small Numbers because of a typographical error. I intended to type a^3 + b^3 + c^3 - 3 a b c and look at its values (Problem A1 on the 2019 Putnam Exam), but I omitted the exponent on $b$ and it came out as a^3 + b^+c^3 - 3 a b c. Mathematica accepted this and interpreted it to mean $a^3 + b^{c^3} - 3 a b c$ and the values Mathematica came up with suggest the latter expression takes on, for nonnegative integer values of $a,b,c$, all integer values except $-6, -14, -18, -20, -30, -36, -38, -48, -50, -60, -66, -74, -78, -96 ...$
The first few terms produced one hit on OEIS:
A108977 $\ $  Numbers $n$ such that $19·n + 17$ is prime.
$0, 6, 14, 18, 20, 30, 36, 38, 44, 48, 50, 74, 78, 84, 98, 104, 108, 116, 120, 126, 140, 144, 146, 158, 168, 174, 176,...$
The first $7$ (nonzero, signless) terms agree and there are some sporadic common entries thereafter. Can anyone offer any explanation?
 A: As Greg Martin notes in a comment, setting $b=1$ or $c=1$ yield special cases $a^3+1-3ac$ and $a^3+b-3ab$ respectively.
In particular, when $c=1$, setting $a=1,2,4$ and letting $b$ vary rule out exactly the congruence classes mod $2$, $5$, and $11$ that would render $19n+17$ divisible by those primes. When $a=b=1$, letting $c$ vary rules out the congruence class of $1$ mod $3$*. (Mod $7$, things fail, as seen with $96$). Note that these restrictions aren't special, and the constants $19$ and $17$ in the OEIS definition are doing the work for us - in a sense, they spend the bits of not-just-a-coincidence credit we built up by finding these specific congruences and terms. So we shouldn't be surprised that this alignment happens.
This gets you most of the way there: below 100, you're left with 0, 6, 8, 14, 18, 20, 26, 30, 36, 38, 44, 48, 50, 54, 56, 60, 66, 74, 78, 80, 84, 86, 96, 98. To get alignment, they just both happen to rule out $8$ and $26$. This much I think is reasonable to chalk up to coincidence, given how often one tries out an obscure series of integers in OEIS; you're bound to get some false positives at this level of significance now and then.
*I'm letting $a,b,c\in\mathbb{Z}$ here, because I think that's what Mathematica was doing - for instance, I can't seem to get $-8$ using nonnegative values, but it's not in the list.
